Question
The equation below was solved incorrectly. Describe the error and solve it correctly
4x-3(x-5)=x
4x-3x+15=x
x+15=x
15=2x
15/2=x
Question 5 options:
x = 15; When moving the x to the right side, they made it 2x when it should have been x
x = -15; When moving the x to the right side, they made it 2x when it should have been - x
No Solution; When moving the x to the right side, they made it 2x when it should have become 0
Infinite Solutions; When moving the x to the right side, they made it 2x when it should have become 0
4x-3(x-5)=x
4x-3x+15=x
x+15=x
15=2x
15/2=x
Question 5 options:
x = 15; When moving the x to the right side, they made it 2x when it should have been x
x = -15; When moving the x to the right side, they made it 2x when it should have been - x
No Solution; When moving the x to the right side, they made it 2x when it should have become 0
Infinite Solutions; When moving the x to the right side, they made it 2x when it should have become 0
Answers
GPT-4o mini
Let's analyze the steps taken in the solution to identify the mistake and solve the equation correctly.
The original equation is:
\[ 4x - 3(x - 5) = x. \]
**Step 1: Distributing the -3**
When distributing -3 in the equation, we have:
\[ 4x - 3(x - 5) = 4x - 3x + 15 = x. \]
So we can rewrite the equation as:
\[ 4x - 3x + 15 = x. \]
**Step 2: Combining like terms**
Now, combining like terms gives us:
\[ x + 15 = x. \]
**Step 3: Subtracting x from both sides**
Subtracting \(x\) from both sides:
\[ x + 15 - x = x - x \]
\[ 15 = 0. \]
This concludes that \(15 = 0\), which is a contradiction. Therefore, the equation has **no solution**.
### Conclusion
The error in the original solution occurred when transitioning from \(x + 15 = x\) to \(15 = 2x\). The correct treatment should result in \(15 = 0\), which indicates that there is no solution.
The correct answer based on the options provided is:
**No Solution; When moving the x to the right side, they made it 2x when it should have become 0.**
The original equation is:
\[ 4x - 3(x - 5) = x. \]
**Step 1: Distributing the -3**
When distributing -3 in the equation, we have:
\[ 4x - 3(x - 5) = 4x - 3x + 15 = x. \]
So we can rewrite the equation as:
\[ 4x - 3x + 15 = x. \]
**Step 2: Combining like terms**
Now, combining like terms gives us:
\[ x + 15 = x. \]
**Step 3: Subtracting x from both sides**
Subtracting \(x\) from both sides:
\[ x + 15 - x = x - x \]
\[ 15 = 0. \]
This concludes that \(15 = 0\), which is a contradiction. Therefore, the equation has **no solution**.
### Conclusion
The error in the original solution occurred when transitioning from \(x + 15 = x\) to \(15 = 2x\). The correct treatment should result in \(15 = 0\), which indicates that there is no solution.
The correct answer based on the options provided is:
**No Solution; When moving the x to the right side, they made it 2x when it should have become 0.**